The Venetian Republic is one of the most important states of the pre-unification history of Italy; further it is the only Italian polity whose lifespan runs from the definitive end of Roman-era institutions to the Napoleonic conquest. The lifespan of the Republic, over one thousand years, is longer than the current British state is separated from the Norman conquest, and the body of academic work on the Republic in each era of its existence is immense. The standard reference work is John Julius Norwich's A History of Venice.

To get you started, I can point you towards these former answers on mine about how the government of the Republic of Venice functioned; this post about the urbanization process of the Venetian lagoon; this post about the Venetian political system as well as this other very similar one; and the conquest of the Republic's mainland possessions as part of a wider answer here; the Venetian military in the 17th century; and an overview of Venice in the 16th century.

Other anecdotes that might interest you are this rather lighthearted description of the War of the League of Cambrai, the first of the Italian wars which centered around the Republic of Venice; this description of 14th century Venetian trade routes; the form of government in 16th century Verona, an important city of the Republic; the 13th century Serrata of the Venetian great council; how the Venetian dalmatian possessions were governed; Venetian glassmaking; Venice during the fourth Crusade; and this answer on the Venetian navy.

It would be worthwhile knowing what books or sources you have looked at.

I ask this because 'Venice, A Maritime Republic' by Frederic C. Lane is referenced by multiple educational institutions in the US so that may be a wise place to start.

The author also has other books you may be interested in.